Fence Patrolling with Two-speed Robots

Czyzowicz, Jurek; Georgiou, Konstantinos; Kranakis, Evangelos; MacQuarrie, Fraser; Pająk, Dominik

doi:10.5220/0005687102290241

Cited by 10 publications

(7 citation statements)

References 21 publications

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“…[13,14,17,18,21]). For other problems considering robots with distinct speeds (e.g., the patrolling problem studied in [16,19,33]), only partial results were obtained. Optimal patrolling using more than two robots on a ring [19], or more than three robots on a segment [33], is unknown in general and all intuitive solutions have been proved sub-optimal for some configurations of the speeds of the robots.…”

Section: Related Workmentioning

confidence: 96%

Linear Search by a Pair of Distinct-Speed Robots

Bampas¹,

Czyzowicz²,

Gąsieniec³

et al. 2016

Structural Information and Communication Complexity

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Two mobile robots are initially placed at the same point on an infinite line. Each robot may move on the line in either direction not exceeding its maximal speed. The robots need to find a stationary target placed at an unknown location on the line. The search is completed when both robots arrive at the target point. The target is discovered at the moment when either robot arrives at its position. The robot knowing the placement of the target may communicate it to the other robot. We look 123Algorithmica for the algorithm with the shortest possible search time (i.e. the worst-case time at which both robots meet at the target) measured as a function of the target distance from the origin (i.e. the time required to travel directly from the starting point to the target at unit velocity). We consider two standard models of communication between the robots, namely wireless communication and communication by meeting. In the case of communication by meeting, a robot learns about the target while sharing the same location with a robot possessing this knowledge. We propose here an optimal search strategy for two robots including the respective lower bound argument, for the full spectrum of their maximal speeds. This extends the main result of Chrobak et al. (in: Italiano, Margaria-Steffen, Pokorný, Quisquater, Wattenhofer (eds) Current trends in theory and practice of computer science, SOFSEM, 2015) referring to the exact complexity of the problem for the case when the speed of the slower robot is at least one third of the faster one. In the wireless communication model, a message sent by one robot is instantly received by the other robot, regardless of their current positions on the line. For this model, we design a strategy which is optimal whenever the faster robot is at most √ 17 + 4 ≈ 8.123 times faster than the slower one. We also prove that otherwise the wireless communication offers no advantage over communication by meeting.

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Section: Related Workmentioning

confidence: 96%

Linear Search by a Pair of Distinct-Speed Robots

Bampas¹,

Czyzowicz²,

Gąsieniec³

et al. 2016

Structural Information and Communication Complexity

Self Cite

View full text Add to dashboard Cite

show abstract

“…In a search-and-rescue version of the problem, the searcher is supposed to bring hider back to the nearest exit in the network. Here the speed of searching is not same as the return speed so, two-speeds [35] are taken into consideration. Other variations include considering turn-time where some time is added to the total cost when the robots make a turn [40].…”

Section: Search Theory and Literature Reviewmentioning

confidence: 99%

“…While here each point is visited multiple times by the searcher, Beachcomber's problem [28] deals with scenario when a point is visited at least once and the focus is to have an algorithm for a fastest search considering two-speeds namely walking speed and searching speed. Other variations include the certain number of robots carrying out the search for a treasure or a hider; patrolling a fence [1], [25], [43], [42], [58], [66], [70] or an area; two-speed robots that have a walking speed and a patrolling speed, each of the multiple two-speed robots have speeds specific to them [30], [28], [35]; robots with distinct maximal speed [30]; two robots on a circular path with multiple exit points [27] search-and-fetch with two robots [56] etc.…”

Section: Search Theory and Literature Reviewmentioning

confidence: 99%

“…They determined the worst-case bound between the fixed and the mobile exit scenarios. In the last decade, evacuation problems are studied with other variations such as multiple exit points [27], exit in a known or unknown domain [2], agents starting from a known [42], [29] or an unknown point, unit or di↵erent speeds of the searchers [35], [42], varied communication methods i.e. face-to-face (F2F) or wireless.…”

Section: Evacuation Problems and Literature Reviewmentioning

confidence: 99%

See 1 more Smart Citation

Worst-case & average-case Efficiency trade-offs for search problems

Sharma¹

2021

Preprint

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Evacuation problems fall under the vast area of search theory and operations research. Problems of evacuation of two robots on a unit disc have been studied for an efficient evacuation time. Work done so far has focused on improving the ’worst-case’ evacuation time with deterministic algorithms. We study the ’average-case’ evacuation time (randomized algorithms) while considering the efficiency trade-off between worst-case and average-case costs. Our other contribution is to analyze average-case and worst-case costs for the cowpath problem (another search problem) which helped us to set a parallel method for the evacuation problem.

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“…In distributed settings, on the other hand, the agents achieve a goal by communicating with each other in different ways, for example, sending messages, leaving tokens, etc. In one distributed approach, Czyzowicz et al [34] showed convergence of a dynamic system of k robots which communicate by merely bouncing against each other. Recently, Pasqualetti et al [76] studied the distributed coordination of a set of moving cameras monitoring a line segment to detect moving intruders.…”

Section: Distributed Patrollingmentioning

confidence: 99%

Coordinated Multi-Agents Patrolling Algorithms

Taleb¹

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We introduce and study various patrolling algorithms using mobile robots. A team of k mobile robots (patrolmen), is deployed on a weighted graph G, in which edge weights represent distances. The robots perpetually move along the domain not exceeding their maximal speed. The robots need to patrol the graph by regularly visiting all points of the domain. The goal of the patrolling problem is to find the perpetual movement of the robots minimizing idle time, which is the maximal time when a point of the graph remains unseen by any robot. In this thesis, we investigate various versions of patrolling problems, in each case attempting to optimize the idle time.In the first scenario, we consider a case where at most f of k robots may be faulty (unreliable), i.e., they do not report their monitoring activities. We design an optimal algorithm for the open curves (segments), and then use these results to study the case of general graphs. We also propose an optimal patrolling strategy for Eulerian graphs. Afterward, we show that computing idle time for three robots, at most one of which is faulty, is NP-hard for some general graphs.Next, we study the patrolling problem by reliable robots, but equipped with distinct visibility ranges, i.e., every robot i has a range of visibility r i representing the distance from its current position, at which the robot can see in each direction. We give the optimal patrolling algorithms for the case of close curves (cycles) and open curves (segments), when all robots have the same maximal speed and different visibility ranges. We also briefly discuss the case where robots have distinct speeds and visibility ranges to show that patrolling by robots equipped with visibility is entirely different than the case of robots with zero visibility. Moreover, we show that patrolling general graphs by robots with the same speed and distinct visibility ranges is NP-hard.Finally, we consider patrolling trees by a team of mobile robots with the same speed and zero visibility. We theoretically show the optimality of an off-line centralized algorithm for trees patrolling. Then, we use these results to experimentally show the efficiency of an on-line distributed algorithm (known as rotor-router) for trees patrolling.ii

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Fence Patrolling with Two-speed Robots

Cited by 10 publications

References 21 publications

Linear Search by a Pair of Distinct-Speed Robots

Linear Search by a Pair of Distinct-Speed Robots

Worst-case & average-case Efficiency trade-offs for search problems

Coordinated Multi-Agents Patrolling Algorithms

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